Answer :
To determine which distribution of data has the largest standard deviation, let's analyze the given distributions and their standard deviations:
1. Data set: \(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)
- Standard Deviation: \(2.6832815729997477\)
2. Data set: \(1, 1, 1, 4, 4, 4, 4, 7, 7, 7\)
- Standard Deviation: \(2.32379000772445\)
3. Data set: \(1, 1, 4, 4, 4, 4, 4, 4, 7, 7\)
- Standard Deviation: \(1.8973665961010275\)
4. Data set: \(1, 4, 4, 4, 4, 4, 4, 4, 4, 7\)
- Standard Deviation: \(1.3416407864998738\)
From these given standard deviations, we can determine that:
- The first data set has the largest standard deviation of \(2.6832815729997477\).
This means that the data set [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex] has the largest standard deviation among the provided distributions. This indicates that the values in this distribution are more spread out from the mean compared to the other data sets.
1. Data set: \(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)
- Standard Deviation: \(2.6832815729997477\)
2. Data set: \(1, 1, 1, 4, 4, 4, 4, 7, 7, 7\)
- Standard Deviation: \(2.32379000772445\)
3. Data set: \(1, 1, 4, 4, 4, 4, 4, 4, 7, 7\)
- Standard Deviation: \(1.8973665961010275\)
4. Data set: \(1, 4, 4, 4, 4, 4, 4, 4, 4, 7\)
- Standard Deviation: \(1.3416407864998738\)
From these given standard deviations, we can determine that:
- The first data set has the largest standard deviation of \(2.6832815729997477\).
This means that the data set [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex] has the largest standard deviation among the provided distributions. This indicates that the values in this distribution are more spread out from the mean compared to the other data sets.
